共查询到18条相似文献,搜索用时 140 毫秒
1.
缓坡方程的推广 总被引:1,自引:1,他引:1
为了描述水波和强烈的环境流在非平整海底上的相互作用,运用无旋运动的Lagrangian变分原理,对经典的Berkhoff缓坡方程进行了改进。假定水流沿水深方向基本上保持均匀性,这正如潮流运动的特征。海底地形由慢变、快变两个分量叠加构成;慢变分量满足缓坡逼近假定,快变分量的波长与表面波波长为同一量级,但其振幅小于表面波的振幅。在以上假定条件下,得到了适用于非平整海底的推广型浅水方程和应用性更加广泛的波-流-非平整海底相互作用的一般缓坡方程,并且从理论上证明一般缓坡方程包含了以下3种著名的缓坡型方程:经典的Berkhoff缓坡方程;波-流相互作用的Kirby缓坡方程、Dingemans关于沙纹海底的缓坡方程。最后,通过与Bragg反射实验数据的比较,表明该模型可以准确地反映快变海底的典型地貌特征。 相似文献
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波-流相互作用的缓坡方程及其波作用量守恒 总被引:1,自引:0,他引:1
当表面波从开阔海域传播至近岸水域时,普遍的波一流相互作用经受着海底的强烈影响.运用水波Hamilton变分原理,建立了近岸水域任意水深变化海底上波一流相互作用的缓坡方程.它可包含波、流和水深一般变化的二阶效应,约化为某些典型的缓坡型方程.据此得出广义程函方程,并且证明该缓坡方程的波作用量守恒. 相似文献
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为刻划近岸波-流-海底相互作用耗散动力系统的多种复杂作用机制,着眼于波浪对近岸大尺度变化环境流作用和考虑多变海底地形(可典型地刻划为由慢变水深和快变水深构成)的影响,由基于黏性流体Navie-Stokes方程的平均流方程,建立了近岸耗散动力系统的广义波作用量守恒方程,从中提出垂向速度波作用量和耗散波作用量这两种新概念,使得它们和经典的波作用量相互间达成了一种互补、协调而又主次分明的更为广泛的守恒形式.从而把波作用量这一经典概念从理想的平均流守恒系统引申到实际的平均流耗散系统(即广义守恒系统)中去,为解释沿岸过程和应用于近海、海岸工程提供了一个理论基础. 相似文献
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基于弹性动力学的线性理论,建立了涂层材料中广义瑞利波传播的理论分析模型,并
且由波动方程和边界条件推导了波的频散方程.分析了慢层和快层对相速度频散的影响,给
出了不同层厚-波长比和不同涂层-基体密度比情况下广义瑞利波相速度的理论解.算例分
析分别比较了慢层和快层结构中波的相速度、群速度,以及随深度衰减的位移与应力振
幅.另外,相速度曲线和位移振幅曲线与文献中给出的结果吻合,验证了理论模型和分析过
程的正确性. 相似文献
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基于饱和多孔介质理论,在固相和液相微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,建立了流体饱和粘弹性多孔介质动力响应的若干Gurtin型变分原理,包括Hu-Washizu变分原理.利用所建立的变分原理,导出了流体饱和粘弹性多孔介质动力响应无网格数值模拟的离散控制方程,此方程是一个关于时间的对称微分方程组,便于分析计算.作为数值例子,研究了流体饱和粘弹性多孔柱体的一维动力响应,数值结果揭示了流体饱和粘弹性多孔柱体中波的传播特性以及固相粘性的影响. 相似文献
9.
波浪引起的海底土层中的应力场和位移场 总被引:4,自引:0,他引:4
本文分析了波浪压力引起的海底土层中孔隙水流动的状况,给出了简化的力学模型来描述海底土层中孔隙水流动所引起的应力场和位移场.对波浪的分析采用了线性波的理论假设,波浪引起的压力计算采用高斯分布理论.孔隙流体和土骨架都假设为可压缩的,孔隙水在海底土层中的流动满足达西定律.由表示质量守恒的连续性方程与应力平衡方程出发,得到了由位移所表示的高阶微分方程,并给出了海底土层中位移场和应力场的解.其解依赖于孔隙流体和土骨架的相对压缩性,土的泊桑比和剪切模量,以及土介质的渗透率和各向异性等特性.文章还结合实际情况进行了计算,并分析了上述参数的影响.对如何应用上述结果提出了相应的参考意见. 相似文献
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非均匀水流中非线性波传播的数值模拟 总被引:1,自引:1,他引:1
以一种考虑波流相互作用的新型{Boussinesq}型方程为控制方程组,
采用五阶{Runge}-{Kutta}-{England}格式离散时间积分,采用七点
差分格式离散空间导数,并通过采用恰当的出流边界条件,从而建立了非均匀水流中非线性
波传播的数值模拟模型. 通过对均匀水流与水深水域内和潜堤地形上存在弱流或强流时波浪
传播的数值模拟,说明模型能有效地反映水流对波浪传播的影响. 相似文献
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IntroductionAccuratemodellingofsurfacewavedynamicsincoastalregionshasbeenthegoalofmuchrecentresearch ,whichhasbeensummarizedinsurveysbyDingemans( 1 997) [1]andKirby( 1 997) [2 ].Therichnessofcoastalwavedynamicsarisesfromthestrongambientcurrentsandthewidevariations… 相似文献
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《European Journal of Mechanics - B/Fluids》2006,25(4):393-405
We prove the existence of a large family of two-dimensional travelling wave patterns for a Boussinesq system which describes three-dimensional water waves. This model equation results from full Euler equations in assuming that the depth of the fluid layer is small with respect to the horizontal wave length, and that the flow is potential, with a free surface without surface tension. Our proof uses the Lyapunov–Schmidt method which may be managed here, contrary to the case of gravity waves with full Euler equations. Our results are in a good qualitative agreement with experimental results. 相似文献
13.
变深度浅水域中非定常船波 总被引:1,自引:0,他引:1
以Green—Naghdi(G—N)方程为基础,采用波动方程/有限元法计算船舶经过变深度浅水域时非定常波浪特性.把运动船舶对水面的扰动作为移动压强直接加在Green-Naghdi方程里,以描述运动船体和水面的相互作用.以Series60 CB=0.6船为算例,给出自由面坡高,波浪阻力在船舶经过一个水下凸包时变化规律,并与浅水方程的结果进行了比较.计算结果表明,当船舶经过凸包时,波浪阻力先增加,后减少,并逐渐趋于正常.同时发现,当船速小于临界速度时(Fr=√gh<1.0),G—N方程给出的船后尾波比浅水方程的结果明显,波浪阻力也比浅水方程的结果有所提高,频率散射必须考虑.当船速大于临界速度时(Fr=√gh>1.0),G—N方程的计算结果与浅水方程差别不大,频率散射的影响可以忽略. 相似文献
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孤立波与多孔介质结构物的非线性相互作用 总被引:1,自引:0,他引:1
基于精确至O(εμ^2,μ^4)的多孔介质无压渗流模型方程和均匀流体质波动的Boussinesq方程,本文对孤立波与多孔介质结构物的相互作用了较系统的数值实验。控制方程采用基于有限差分方程离散,在时域上采用了预估-校正方法进行了时间积分。在求解演化方程的过程中,引入“内迭代”过程实现流体域和多孔介质交界面的连接条件。结果表明孤立波在多孔介质上的反射与在不可渗透的界面上的反射类似,形成反向的孤立波但 相似文献
16.
S. A. Gaponov N. M. Terekhova 《Journal of Applied Mechanics and Technical Physics》2009,50(5):733-741
Interactions of disturbances in a hypersonic boundary layer on a porous surface are considered within the framework of the
weakly nonlinear stability theory. Acoustic and vortex waves in resonant three-wave systems are found to interact in the weak
redistribution mode, which leads to weak decay of the acoustic component and weak amplification of the vortex component. Three-dimensional
vortex waves are demonstrated to interact more intensively than two-dimensional waves. The feature responsible for attenuation
of nonlinearity is the presence of a porous coating on the surface, which absorbs acoustic disturbances and amplifies vortex
disturbances at high Mach numbers. Vanishing of the pumping wave, which corresponds to a plane acoustic wave on a solid surface,
is found to assist in increasing the length of the regions of linear growth of disturbances and the laminar flow regime. In
this case, the low-frequency spectrum of vortex modes can be filled owing to nonlinear processes that occur in vortex triplets. 相似文献
17.
An analytical theory is presented for the low-frequency behavior of dilatational waves propagating through a homogeneous elastic
porous medium containing two immiscible fluids. The theory is based on the Berryman–Thigpen–Chin (BTC) model, in which capillary
pressure effects are neglected. We show that the BTC model equations in the frequency domain can be transformed, at sufficiently
low frequencies, into a dissipative wave equation (telegraph equation) and a propagating wave equation in the time domain.
These partial differential equations describe two independent modes of dilatational wave motion that are analogous to the
Biot fast and slow compressional waves in a single-fluid system. The equations can be solved analytically under a variety
of initial and boundary conditions. The stipulation of “low frequency” underlying the derivation of our equations in the time
domain is shown to require that the excitation frequency of wave motions be much smaller than a critical frequency. This frequency
is shown to be the inverse of an intrinsic time scale that depends on an effective kinematic shear viscosity of the interstitial
fluids and the intrinsic permeability of the porous medium. Numerical calculations indicate that the critical frequency in
both unconsolidated and consolidated materials containing water and a nonaqueous phase liquid ranges typically from kHz to
MHz. Thus engineering problems involving the dynamic response of an unsaturated porous medium to low excitation frequencies
(e.g., seismic wave stimulation) should be accurately modeled by our equations after suitable initial and boundary conditions
are imposed. 相似文献
18.
The motion of turbulent Stokes waves on a finite constant depth fluid with a rough bed is considered. First and second order
turbulent boundary layer equations are solved numerically for a range of roughness parameters, and from the solutions are
calculated the mass transport velocity profiles and attenuation coefficients. A new mechanism of turbulent mass transport
is found which predicts a reduction and reversal of drift velocity in shallow water in agreement with experimental observations
under turbulent conditions. This transpires because the second order Stokes wave motion, in a turbulent boundary layer, can
directly influence the mass transport velocity by mode coupling interactions between different second order Fourier modes
of oscillation. It is also found that the Euler contribution due to the radiation stress of the first order motion is reduced
to half of it's corresponding laminar value as a consequence of the velocity squared stress law. The attenuation is found
to be of inverse algebraic type with the reciprocal wave height varying linearly with either distance or time. The severe
wave height restriction applicable to the Longuet-Higgins [4] solution is shown not to apply to progressive waves on a finite
constant depth of fluid. The existence of sand bars on sloping beaches exposed to turbulent waves is predicted. 相似文献